This is exactly why I tried to restate the situation in terms of the more precise concept of “mutual information” in Richard’s last topic, although I guess I was a bit vague at points as to how it works.
So in the context of Bayesian inference, and rationality in general, we should start with:
“A controller has a model (explicit or implicit) of it’s environment iff there is mutual information between the controller and the environment.”
This statement is equivalent to:
“A controller has a model (explicit or implicit) of its environment iff, given the controller, you require a shorter message to describe its environment (than if you could not reference the controller).”
From that starting point, the question is easier to answer. Take the case of the thermostat. If the temperature sensor is considered part of this controller, then yes, it has a model of its environment. Why? Because if you are given the sensor reading, you can more concisely describe the environment: “That reading, plus a time/amplitude shift.”
Richard puts a lot of emphasis on how cool it is that the thermostat doesn’t need to know if the sun is shining. This point can be rephrased as:
“A controller does not need to have mutual information with all of its environment to work.” Or,
“Learning a controller, and the fact that it works, does not suffice to tell you everything about its environment.”
I think that statement sums up what Richard is trying to say here.
And of course you can take this method further and discuss the mutual information between a) the controller, b) the output, c) the environment. That is, do a) and b) together suffice to tell you c)?
This is exactly why I tried to restate the situation in terms of the more precise concept of “mutual information” in Richard’s last topic, although I guess I was a bit vague at points as to how it works.
So in the context of Bayesian inference, and rationality in general, we should start with:
“A controller has a model (explicit or implicit) of it’s environment iff there is mutual information between the controller and the environment.”
This statement is equivalent to:
“A controller has a model (explicit or implicit) of its environment iff, given the controller, you require a shorter message to describe its environment (than if you could not reference the controller).”
From that starting point, the question is easier to answer. Take the case of the thermostat. If the temperature sensor is considered part of this controller, then yes, it has a model of its environment. Why? Because if you are given the sensor reading, you can more concisely describe the environment: “That reading, plus a time/amplitude shift.”
Richard puts a lot of emphasis on how cool it is that the thermostat doesn’t need to know if the sun is shining. This point can be rephrased as:
“A controller does not need to have mutual information with all of its environment to work.” Or,
“Learning a controller, and the fact that it works, does not suffice to tell you everything about its environment.”
I think that statement sums up what Richard is trying to say here.
And of course you can take this method further and discuss the mutual information between a) the controller, b) the output, c) the environment. That is, do a) and b) together suffice to tell you c)?
EDIT: Some goofs